Problem 2.

Let ABCD be a convex quadrilateral. Let the circles be constructed on the segments AB and CD as their diameters touch externally at the point M, which is different from the point of intersection of the diagonals of the quadrilateral. Let the circle passing through the points A, M, and C, intersects the line connecting the point M and the middle point of AB in the point K, and let the circle passing through the points B, M, and D, intersects the same line in the point L. Then | MK-ML | = | AB-CD |.
The data handling can be started in different ways.